Finding Robust Solutions to Stable Marriage

Abstract: We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An $(a,b)$-supermatch is a stable matching in which if $a$ pairs break up it is possible to find another stable matching by changing the partners of those $a$ pairs and at most $b$ other pairs. In this context, we define the most robust stable matching as a $(1,b)$-supermatch where b is minimum. We show that checking whether a given stable matching is a $(1,b)$-supermatch can be done in polynomial time. Next, we use this procedure to design a constraint programming model, a local search approach, and a genetic algorithm to find the most robust stable matching. Our empirical evaluation on large instances show that local search outperforms the other approaches.